Question

determine the mean, median, mode, and mid - range for this collection of class test scores: 88 82 97 76 79 92 65 84 79 90 75 82 78 77 93 88 95 73 69 89 93 78 60 95 88 72 80 94 88 74 a. mean is 84, median is 82, mode is 82, mid - range is 77 b. mean is 82, median is 88, mode is 88, mid - range is 77 c. mean is 82.4, median is 88, mode is 82, mid - range is 78.5 d. mean is 82.4, median is 82, mode is 88, mid - range is 78.5 please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

First, sum all the scores: \(88 + 82+97 + 76+79+92+65+84+79+90+75+82+78+77+93+88+95+73+69+89+93+78+60+95+88+72+80+94+88+74\) = \(2472\). There are \(n = 30\) scores. The mean \(\bar{x}=\frac{2472}{30}=82.4\).

Step2: Calculate the median

Arrange the scores in ascending - order: \(60,65,69,72,73,74,75,76,77,78,78,79,79,80,82,82,84,88,88,88,88,89,90,92,93,93,94,95,95,97\). Since \(n = 30\) (an even number), the median is the average of the \(\frac{n}{2}=15\)th and \((\frac{n}{2}+1)=16\)th ordered values. The 15th value is \(82\) and the 16th value is \(82\), so the median \(\frac{82 + 82}{2}=82\).

Step3: Calculate the mode

The mode is the number that appears most frequently. The number \(88\) appears \(4\) times, more frequently than any other number, so the mode is \(88\).

Step4: Calculate the mid - range

The mid - range is calculated as \(\frac{\text{highest value}+\text{lowest value}}{2}\). The highest value is \(97\) and the lowest value is \(60\). So the mid - range is \(\frac{97 + 60}{2}=\frac{157}{2}=78.5\).

Answer:

D. Mean is 82.4, median is 82, mode is 88, midrange is 78.5